If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?

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If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD \(\,= 60^\circ\)
(2) AC = 12

Answer: C

Source: Manhattan GMAT

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Vincen wrote:
Sun Dec 26, 2021 10:18 am
2.jpg

If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD \(\,= 60^\circ\)
(2) AC = 12

Answer: C

Source: Manhattan GMAT
1) is not sufficient

The left triangle becomes a \(90-30-60\) triangle however we don't know anything about the right triangle. \(\Large{\color{red}\chi}\)

2) is not sufficient

The right triangle becomes a \(90-30-60\) triangle however we don't know anything about the left triangle. \(\Large{\color{red}\chi}\)

Combining \(1 \& 2\) is sufficient
We know both the triangles are \(90-30-60\) with same sides. \(\Large{\color{green}\checkmark}\)

Hence, C